Horizontal motions of a tanker attached to a single-point mooring (SPM) terminal were predicted using digital simulation in the time domain. Excitations from steady current, gusting wind, and irregular seaway were included. Hydrodynamic forces generated by the ship’s motion and the action of its propeller and rudder were calculated in accordance with a previously validated, nonlinear quasi-steady four-quadrant maneuvering model, extended to include linear memory effects due to waves generated by the moving ship. Memory effects were approximated by a vectorial recursive state space model corresponding to a set of higher order differential equations. A nonlinear relationship of the force in the mooring hawser was assumed to represent restoring force characteristics of the SPM system. Wave excitation forces comprised first-order forces at wave frequencies and second-order drift forces at low frequencies. First-order wave forces were obtained by superposition of force components corresponding to regular wave components comprising the wave spectrum. Based on the low-frequency wave envelope, drift forces were calculated using mean drift force coefficients in regular waves. Selected sample simulations are presented to illustrate the use of this digital simulation method.